{"id":12708,"date":"2023-01-07T21:08:31","date_gmt":"2023-01-07T15:38:31","guid":{"rendered":"https:\/\/mathemerize.com\/?p=12708"},"modified":"2023-01-07T21:08:35","modified_gmt":"2023-01-07T15:38:35","slug":"the-distribution-below-gives-the-weights-of-30-students-of-a-class-find-the-median-weight-of-the-students","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-distribution-below-gives-the-weights-of-30-students-of-a-class-find-the-median-weight-of-the-students\/","title":{"rendered":"The distribution below gives the weights of 30 students of a class. Find the median weight of the students."},"content":{"rendered":"\n

Question :<\/h2>\n\n\n\n
Weight in (kg)<\/td>40 – 45<\/td>45 – 50<\/td>50 – 55<\/td>55 – 60<\/td>60 – 65<\/td>65 – 70<\/td>70 – 75<\/td><\/tr>
Number of students<\/td>2<\/td>3<\/td>8<\/td>6<\/td>6<\/td>3<\/td>2<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Solution :<\/h2>\n\n\n\n

We prepare the following table to compute the median :<\/p>\n\n\n\n

Weight in (kg)<\/td>Number of students (frequency)<\/td>Cumulative Frequency<\/td><\/tr>
40 – 45<\/td>2<\/td>2<\/td><\/tr>
45 – 50<\/td>3<\/td>5<\/td><\/tr>
50 – 55<\/td>8<\/td>13<\/td><\/tr>
55 – 60<\/td>6<\/td>19<\/td><\/tr>
60 – 65<\/td>6<\/td>25<\/td><\/tr>
65 – 70<\/td>3<\/td>38<\/td><\/tr>
70 – 75<\/td>2<\/td>30<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

We have : n = 30, So, \\(n\\over 2\\) = 15<\/p>\n\n\n\n

The cumulative frequency just greater than \\(n\\over 2\\) is 19 and the corresponding the class is (55 – 60).<\/p>\n\n\n\n

Thus, (55 – 60) is the median class such that \\(n\\over 2\\) = 15, l = 55, f = 6, cf = 13 and h = 5.<\/p>\n\n\n\n

Substituting these values in the formula,<\/p>\n\n\n\n

Median = l + (\\({n\\over 2} – cf\\over f\\))(h)<\/p>\n\n\n\n

= 55 + (\\(15 – 13\\over 6\\))(5) = 55 + \\(2\\over 6\\)(5) = 55 + 1.67 = 56.67<\/p>\n\n\n\n

Hence, the median weight is 56.67<\/strong> kg<\/p>\n","protected":false},"excerpt":{"rendered":"

Question : Weight in (kg) 40 – 45 45 – 50 50 – 55 55 – 60 60 – 65 65 – 70 70 – 75 Number of students 2 3 8 6 6 3 2 Solution : We prepare the following table to compute the median : Weight in (kg) Number of students (frequency) …<\/p>\n

The distribution below gives the weights of 30 students of a class. Find the median weight of the students.<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,58],"tags":[],"yoast_head":"\nThe distribution below gives the weights of 30 students of a class. 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